The first time I solved this problem, I did it in a way that I had to
mess with changing fractions to common denominators and all that.
Suddenly, however, the clean and easy way to do it dawned on me.
Here it is:
-- There are 56 marble in the bag.
-- The probability of pulling a red marble is 5/8, so
5/8 of the 56 marbles must be red.
5/8 of 56 = 35 red marbles.
-- The probability of pulling a green marble is 1/7,
so 1/7 of the 56 marbles must be green.
1/7 of 56 = 8 green marbles.
-- The red and green marbles make up (35 + 8) = 43
of the 56 marbles in the bag.
-- The rest of them are yellow.
There are (56 - 43) = 13 yellow marbles in the bag.
-- The probability of pulling a yellow marble is 13/56 . (about 23.2%)
No messy fractions at all !
That's the way I like it !